Changed Identity. The first thing you need to realise is that this is NOT you being unreasonable, irrationally insecure or jealous. What you're feeling is entirely appropriate and normal. It might help you to browse a few of the threads on here about men who are doing just as your DP is.
Men often don't think that emotional affairs are particularly dangerous, because they equate infidelity with sex. If that hasn't happened (yet), they can delude themselves that this is just a bit of escapist fun and therefore they feel no guilt.
Guilt kicks in when all this is discovered - it's at this point that they are forced to accept it's "wrong", but the trouble is they don't really believe that it is - and to an extent, they are already addicted to it and would find it hard to give it up. So they continue with this delusion that it's harmless fun, until there comes a tipping point. This is when they suddenly stop deluding themselves that this isn't going to result in an affair and they acknowledge that this is what they do want after all.
It's a slippery slope, believe me and the things both of you might need to acknowledge are:
Why he is doing it - it doesn't sound like this has been explored.
He might pretend he is keeping information from you to protect you, but what this really means is that he's still addicted to it all, has no intention of giving it up and if you knew about it, he'd be forced to.
Someone who is not a "friend of the marriage/relationship" is not a friend at all. Women or men who engage in inappropriate texts with an attached person do not wish the primary relationship well, believe me!
Hecate was on another thread last night saying that the term "emotional affair" is a load of old bunkum - what it is really a prelude to sex. I think she's right, by and large. It takes a wise person to acknowledge that this is what it is and to back away before more harm is done - but the trouble is, too many people fail to acknowledge what it is, because no sex has yet taken place.
By the time sex DOES take place, it is almost too late. An emotional affair with sex is the really dangerous territory.
Finally, might help you to read a book called "Not Just Friends" by Dr. Shirley Glass. And one of my conditions would be to get your DP to read it. Stand back and watch the scales fall from his eyes when he realises just what he has been doing.